State whether the following proof (by mathematical induction) is true or false for the statement. P(n): 12 + 22 + ... + n2 = n(n+1)(2n+1)6 Proof By the Principle of Mathematical induction - Mathematics

Question

State whether the following proof (by mathematical induction) is true or false for the statement.

P(n): 1² + 2² + ... + n² = `(n(n + 1) (2n + 1))/6`

Proof By the Principle of Mathematical induction, P(n) is true for n = 1,

1² = 1 = `(1(1 + 1)(2*1 + 1))/6`. Again for some k ≥ 1, k² = `(k(k + 1)(2k + 1))/6`. Now we prove that

(k + 1)² = `((k + 1)((k + 1) + 1)(2(k + 1) + 1))/6`

Options

True
False

MCQ

True or False

Solution

This statement is False.

Explanation:

Since in the inductive step both the inductive hypothesis and what is to be proved are wrong.

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Principle of Mathematical Induction

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Q 15 Q 14 Q 1

Chapter 4: Principle of Mathematical Induction - Solved Examples [Page 70]

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NCERT Exemplar Mathematics [English] Class 11

Chapter 4 Principle of Mathematical Induction
Solved Examples | Q 15 | Page 70

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